Given n > 3, find number of diagonals in n sided convex polygon.
According to Wikipedia, In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal.
Examples :
Input : 5 Output : 5
Explanation: Five possible diagonals are : AC, AD, BD, BE, CE
Since for an n-sided convex polygon, from each vertex, we can draw n-3 diagonals leaving two adjacent vertices and itself. Following this way for n-vertices, there will be n*(n-3) diagonals but then we will be calculating each diagonal twice so total number of diagonals become n*(n-3)/2
Here is code for above formula.
C++
#include <iostream>using namespace std;// C++ function to find number of diagonals// in n sided convex polygonint numberOfDiagonals(int n){ return n * (n - 3) / 2;}// driver code to test above functionint main(){ int n = 5; cout << n << " sided convex polygon have "; cout << numberOfDiagonals(n) << " diagonals"; return 0;} |
Java
// Java function to find number of diagonals// in n sided convex polygonpublic class Diagonals { static int numberOfDiagonals(int n) { return n * (n - 3) / 2; } // driver code to test above function public static void main(String[] args) { int n = 5; System.out.print(n + " sided convex polygon have "); System.out.println(numberOfDiagonals(n) + " diagonals"); }}// This code is contributed by Saket Kumar |
Python3
# Python3 program to find number of diagonals# in n sided convex polygondef numberOfDiagonals(n): return n * (n - 3) / 2 # driver code to test above functiondef main(): n = 5 print(n , " sided convex polygon have ") print(numberOfDiagonals(n) , " diagonals")if __name__ == '__main__': main()#this code contributed by 29AjayKumar |
C#
// C# function to find number of diagonals// in n sided convex polygonusing System;class GFG { static int numberOfDiagonals(int n) { return n * (n - 3) / 2; } // driver code to test above function public static void Main() { int n = 5; Console.Write(n + " sided convex polygon have "); Console.WriteLine(numberOfDiagonals(n) + " diagonals"); }}// This code is contributed by Sam007 |
PHP
<?php// PHP function to find number// of diagonals in n sided// convex polygonfunction numberOfDiagonals($n){ return $n * ($n - 3) / 2;}// Driver Code$n = 5;echo $n , " sided convex polygon have ";echo numberOfDiagonals($n) , " diagonals"; // This code is contributed by aj_36?> |
Javascript
<script>// Javascript function to find number of // diagonals in n sided convex polygonfunction numberOfDiagonals(n){ return n * (n - 3) / 2;}// Driver codevar n = 5;document.write(n + " sided convex polygon have ");document.write(numberOfDiagonals(n) + " diagonals");// This code is contributed by Ankita saini</script> |
Output :
5 sided convex polygon have 5 diagonals
Time Complexity: O(1)
Auxiliary Space: O(1)
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